Tensioning devices of the type to which the present invention relate are not new per se. German patent application No. P 3,536,834 discloses a tensioning device including a support arm designed as a lever which mounts a tensioning roll at one end and at its opposite end is attached by way of a pivot bearing to a machine block. A mounting plate is disposed between the machine block and pivot bearing and secured by a common fastener screw. A linear-action spring/damper mechanism is supported on the mounting plate or in the installed state on the machine block by an additional screw fastener. The spring/damper mechanism urges the tensioning roll against the drive belt via the support arm. The damper functions to damp oscillations of the drive belt or impact loads acting on the tensioning roll. The tensioning device consists, before assembly, of essentially three individual components; the mounting plate, the support arm with tensioning roll and the spring/damper mechanism which, in the uninstalled state, is quite elongated since the spring is fully relaxed. When the components are assembled, the spring/damper mechanism first must be tensioned and installed in this state together with the other components. This installation procedure is rather tedious and time-consuming and thus, it would be desirable to have a pre-mounted unit. In that case, however, the strength of the spring causes the components to be skewed with respect to each other. Further, it has been observed that particularly in the area of the pivot bearing, the fastener screw, which is merely inserted through the attachment hole in the mounting plate, provides an extremely unstable joint since the parts are held together merely by the slant of the screw. The components are disposed in their functional positions only after installation and only then can they operate satisfactorily.